BERLIN, June 4 (Reuters) - Europe's biggest online fashion retailer Zalando plans to expand to Ireland and the Czech Republic and could add other markets later, but does not expect profitability to increase for years as it invests heavily in logistics and technology.

"We will not see increases in profitability for the coming years," co-Chief Executive Rubin Ritter told an annual strategy day, adding that a long-term target for an operating profit margin of 10 percent had been pushed further out.

A spokesman said Zalando had not changed its mid-term target for no increase in its operating margin until 2020.

As Amazon has made a big push into fashion, Zalando last year pared its profit forecast as it spends on new warehouses, marketing and improving personalisation.

Zalando's shares fell 2 percent to 44.50 euros in midmorning trade, underperforming the MDAX index, which was up 0.2 percent.

"It would not be very smart to stop focusing on growth," Ritter said, noting that Zalando still only had 1 percent of a fragmented European fashion market worth 420 billion euros ($493 billion).

Zalando had already announced in February the plan to open online stores in two new countries this year, but did not say which ones. On Tuesday, it said Ireland and the Czech Republic would be served by its existing warehouses from this summer.

Ritter said Zalando could also expand to other markets in coming years, noting the retailer did not have a site in Portugal or much of eastern Europe.

However, he said Zalando had no plans for major investments in Britain, where it has a relatively small presence, due to concerns about possible import tariffs and the fluctuation of the pound after the country leaves the European Union.

Launched in Berlin in 2008, Zalando has grown fast to sell almost 2,000 brands in 15 countries, mostly in western Europe, but has not added a new market since Luxembourg in 2013.

Zalando said it would add the Monki brand of Sweden's H&M in August, the third H&M brand it will sell after Weekday and Cheap Monday.

It will also launch an English version of its site in Germany and an Italian version in trilingual Switzerland.

Last month, Zalando said the launch of beauty products in Germany had made a promising start and its active customer numbers jumped in the first quarter but a late start to spring hit profitability.

British rival ASOS has also said it will have to step up spending on technology and logistics, with the extra costs taking a toll on its elevated share price. ($1 = 0.8524 euros) (Reporting by Emma Thomasson Editing by Maria Sheahan/Keith Weir)